具有潜伏和隔离的传染病模型的全局稳定性

研究了一类具有隔离仓室和潜伏仓室的非线性高维自治微分系统SEQIJR传染病模型，得到疾病绝灭与否的阀值一基本再生数R0．证明了当R0≤1时，模型仅存在无病平衡点，且无病平衡点是全局渐近稳定的，疾病最终绝灭；当R0〉1时，模型存在两个平衡点，无病平衡点不稳定，地方病平衡点全局渐近稳定，疾病将持续．隔离措施影响着基本再生数，进而推得结论：适当地增大隔离强度，将有益于有效地控制疾病的蔓延．这就从理论上揭示了隔离对疾病控制的积极作用．

The Global Stability of the Epidemic Model with Latency and Quarantine

In this paper, a class of non-linear high dimensional autonomous SEQIJR epidemiology model containing quarantine is studied. The threshold, basic reproductive number, which determines whether a disease is extinct or not is obtained. The existence and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved. The conclusions indicate that a proper increasing of segregation intension benefits the efficient restraining disease spread. It is theoretically showed that the segregation has an active effect on disease controlling.